Suppose that you have three vectors: f1 (x) = 1, f2 (x) = x – 1, and f3 (x) = } (x² – 4x + 2), that make up an orthonormal basis spanning the real vector space of quadratic functions with the inner product: (fi | f;) = ° fi (x) f; (x) e-²dx. Suppose we have a derivative operator D = . What is (f3 |D| f2) =? 5/8 -3/4 O 000
Suppose that you have three vectors: f1 (x) = 1, f2 (x) = x – 1, and f3 (x) = } (x² – 4x + 2), that make up an orthonormal basis spanning the real vector space of quadratic functions with the inner product: (fi | f;) = ° fi (x) f; (x) e-²dx. Suppose we have a derivative operator D = . What is (f3 |D| f2) =? 5/8 -3/4 O 000
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Transcribed Image Text:Suppose that you have three vectors: fi (x) = 1, f2 (x) = x
quadratic functions with the inner product: (f; | f;) = [° fi (x) f; (x) e¯ªdx. Suppose we have a derivative operator D = . What is (f3 |D| f2) =?
1, and f3 (x) =; (x² – 4x + 2), that make up an orthonormal basis spanning the real vector space of
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dx
1
5/8
-3/4
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